Ruled Surfaces according to Rotation Minimizing Frame

Abstract

In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is developable. Also, we give some new results and theorems related to be the asymptotic curve, the geodesic curve and the line of curvature of the base curve on the ruled surface.

On the trajectory ruled surfaces of framed base curves in the Euclidean space

“…So trajectory ruled surfaces are one of the most important topics of ruled surface theory to study spatial mechanism and space kinematic. For more details on ruled surfaces and its applications, see previous studies 1–6 …”

“…For more details on ruled surfaces and its applications, see previous studies. [1][2][3][4][5][6] In differential geometry, the curve theory is highly important and a classical subject. Generally, geometers consider regular curve, if they work on curve theory.…”